The Government’s chief whip was threatened with arrest after allegedly calling an officer a “moron” and saying that it was “best learn you learn your f------ place” after he was told he could not cycle out of the main gates of Downing Street.

Mr Mitchell admitted he had not “treated the police with the respect they deserve”. However he insisted he had not "used the words that have been reported". His friends specifically denied he called officers plebs or morons.

But Mr Mitchell’s claims were challenged last night by rank and file police officers, who stood by the account given by the Downing Street officer who was insulted by Mr Mitchell.

John Tully, chairman of the Metropolitan Police Federation, said: “I know what the officers have told me, and what was reported … is absolutely what happened. I think Mr Mitchell needs to address his position and resign as soon as possible.

“Someone who holds such high office, and who apparently holds the police in such contempt, is not deserving of such high office and he should resign.”

Paul McKeever, the chairman of the Police Federation of England and Wales, asked why Mr Mitchell was allowed to remain in Government.

“It is hard to fathom how someone who holds the police in such contempt could be allowed to hold a public office.

“Mr Mitchell’s half-hearted apology for the comments made whilst leaving Downing Street will do little to build bridges with the police who feel they have once again been treated with a lack of respect and civility by members of this government.”

Boris Johnson, the London Mayor who is in charge of policing in the capital, failed to back Mr Mitchell. Asked if he should resign, his spokesman said it was a “matter for the Prime Mitchell and Mr Mitchell”.

Last year Mr Johnson said that anyone who swore at the police should “expect” to be arrested, adding: “If people feel there are no comebacks, no boundaries, no retribution for the small stuff, then they will go on to commit worse crimes.”

Labour also piled the pressure on Mr Mitchell. Shadow home secretary Yvette Cooper said the reported outburst was an “utter disgrace”, and questioned how Mr Mitchell could do the job of chief whip if he could not keep his temper in check.

The incident, which was reported in Downing Street’s police log, occurred on Wednesday evening. Friends said he had been allowed to cycle out of the main gate on three occasions that day.

He also reportedly said: “Open this gate, I’m the Chief Whip. I’m telling you - I’m the Chief Whip and I’m coming through these gates.”

Last night, the Government was trying to control the escalating row. Policing minister Damian Green spoke to Mr McKeever about the affair.

CCTV footage reportedly existed of the altercation, but there was no audio recording. Downing St said it was “policy that we do not release CCTV footage for security reasons”.

Prime Minister David Cameron, on a visit to Manchester after two female police officers were murdered this week, said Mr Mitchell’s remarks were “wrong “and “not appropriate” and that it was “right he’s apologised”.

Mr Cameron said: “The police do an outstanding job across our country. They do a very important job protecting places like Number 10 Downing Street.

“I’m very conscious of the protection they give to me and my family, and the work that they do for everyone in public life.”

Mr Mitchell apologised both to the duty sergeant and to the officer concerned in a phone call, before reportedly pulling out of a speaking engagement in Reading.

The minister said sorry for not giving the police “the respect they deserve” but he denied using abusive language.

Mr Mitchell said in a statement: “I attempted to leave Downing Street via the main gate, something I have been allowed to do many times before.

“I was told that I was not allowed to leave that way. While I do not accept that I used the words that have been reported, I accept I did not treat the police with the respect they deserve.

“I have seen the supervising sergeant and apologised and will also apologise to the police officer involved.”